Which of these numbers is prime? ${35,\ 49,\ 81,\ 96,\ 97}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 35 are 1, 5, 7, and 35. The factors of 49 are 1, 7, and 49. The factors of 81 are 1, 3, 9, 27, and 81. The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96. The factors of 97 are 1 and 97. Thus, 97 is a prime number.